Let $k$ be a finite field, and $A$, $B$ abelian varieties over $k$. Let $T_p(A)$, $T_p(B)$ be the (contravariant) Dieudonn'e modules associated to the p-divisible groups attached to $A$ and $B$, respectively. The theorem of Tate in the question is that the natural map

${\rm Hom}_k(A,B)\otimes\mathbf{Z}_p\longrightarrow{\rm Hom}(T_p(B),T_p(A))$

is an isomorphism.

It seems to me that the standard reference for the proof of this theorem is a paper of Tate titled $\textit{Endomorphisms of abelian varieties over finite fields. II}$ that should have appeared 50 years ago in Inventiones but, I am right, never did.

Is there another reference in the literature for the proof of this theorem?

Thanks.

Let $k$ be a finite field, and $A$, $B$ abelian varieties over $k$. Let $T_p(A)$, $T_p(B)$ be the (contravariant) Dieudonn'e modules associated to the p-divisible groups attached to $A$ and $B$, respectively. The theorem of Tate in the question is that the natural map

${\rm Hom}_k(A,B)\otimes\mathbf{Z}_p\longrightarrow{\rm Hom}(T_p(B),T_p(A))$

is an isomorphism.

It seems to me that the standard reference for the proof of this theorem is a paper of Tate titled Endomorphisms of abelian varieties over finite fields. II that should have appeared 50 years ago in Inventiones but, I am right, never did.

Is there another reference in the literature for the proof of this theorem?

Thanks.

Let $k$ be a finite field, and $A$, $B$ abelian varieties over $k$. Let $T_p(A)$, $T_p(B)$ be the (contravariant) Dieudonn'e modules associated to the p-divisible groups attached to $A$ and $B$, respectively. The theorem of Tate in the question is that the natural map

${\rm End}_k(A,B)\otimes\mathbf{Z}_p\longrightarrow{\rm End}(T_p(B),T_p(A))$

is an isomorphism.

It seems to me that the standard reference for the proof of this theorem is a paper of Tate titled $\textit{Endomorphisms of abelian varieties over finite fields. II}$ that should have appeared 50 years ago in Inventiones but, I am right, never did.

Is there another reference in the literature for the proof of this theorem?

Thanks.

Let $k$ be a finite field, and $A$, $B$ abelian varieties over $k$. Let $T_p(A)$, $T_p(B)$ be the (contravariant) Dieudonn'e modules associated to the p-divisible groups attached to $A$ and $B$, respectively. The theorem of Tate in the question is that the natural map

${\rm Hom}_k(A,B)\otimes\mathbf{Z}_p\longrightarrow{\rm Hom}(T_p(B),T_p(A))$

is an isomorphism.

It seems to me that the standard reference for the proof of this theorem is a paper of Tate titled $\textit{Endomorphisms of abelian varieties over finite fields. II}$ that should have appeared 50 years ago in Inventiones but, I am right, never did.

Is there another reference in the literature for the proof of this theorem?

Thanks.